A Self Consistent Joint Extraction of 0 and RCX

for HICUM6th European Hicum Workshop

12-13 June 05, ATMEL in Heilbronn

Zoltan Huszka austriamicrosystems AG

Purpose

• Proposal for a new 0 & RCX extraction

• Demonstration of the results

• Lowlights and Highlights

Outline

• Former RCX extraction methods

• Overview of the existing 0 extraction methods

• Theory of joint extraction for both parameters

• Extraction procedure

• Extraction results

• Summary

A Few Known RCX Extraction Methods

• Forced beta (Logan_1971)

• Isub (Berkner_1994)

• Solution of Parasitic pnp (Paasschens_2001)

• Special test structures (Schroeter_1991)

• Modified forced beta (Wu_2004)

• 2D numerical calculations (Kaufmann_ 2005)

• Corrected Inverse FT vs. VT/Ic (Schroeter_1991)

• Refined Inverse FT vs. VT/Ic (Ardouin_2001)

• Inverse FT vs. 1/gm (Malorny_2002)

• 3-variate linear regression (Fregonese_2006)

0 Extraction Methods

Existing Concept of 0 Extraction

T

cjcxjc

jcxjcBE

Tf V

IgmCCRERCX

gm

CCC :ionapproximat);()(

1

0 is the zero intercept for infinite Ic

• Key model parameters must be formerly known• Correct magnitude of RCX is critical• Internal collector time constant is omitted• The formula is approximative only

A Novel Concept

rbx rbi rc i rcxcjc

cjep

rpicpi

ro

re

cjcp

rs

gm*vbeivbei

1

3

2

34

B C

E E

• Extract intrinsic FT of block#1 with nonzero rci

• Apply result to HICUM

Block Transformations (1)

Unilateralized (UL) two-port parameters:

22

21

11

2121

1111

1221211212212112

~

~

~

~~~1~

~~~~

z

z

y

yh

yh

zzzzzzyyyyyy iiiiiiii

Consequently: )2(21

)3(21

)2(11

)3(11

~~~~ yyyy

With :

Dividing :

)1()1()1()1(

)1(21)2(

21)1()1(

)1()1(11)2(

11

~~~

YZYZYZ

Y

gmyy

rciyy b

bb

b0)1(12 by

)1(1)1(

~1

)1(21

)1(22

)1(11

)1()1(11

)3(21

rcicjcjhgm

yrciy

gm

rciy

h b

bb

b

Y

)1(1

~1

)1(21

)3(21

rcicjcjhh bb

Block Transformations (2)

Starting from the outside:

RELATION OF RAW AND INTRINSIC UL BETA

)4(12

)4(21

)3(12

)3(22

)4(12

)4(21

)4(12

)4(22

)4(21

~1

bb

bb

bb

bb

b zz

RCXzz

zz

zz

h

)4(

21)3(

21)4(

21~~

1~

1

bbb z

RCX

hh

)4(21

)1(21

)1(21

)4(21

~1

~1

bbbb z

RCX

h

rcicjcj

hh

The intrinsic transistor has a single pole ac beta:

)1()1()1(021

)1(21

111

TTbb

jjhh

Determining RCX

RCX can be expressed from the first equation

)4(21

)1(2

)4(21

)4(21

)1()4(21

~1

1~1

~11

~1

bTb

bTb

zRCX

cjcrci

h

zRCXcjcrci

h

)4(21

)1(21

)1(21

)4(21

~1

~1

bbbb z

RCX

h

rcicjcj

hh

)4(21

)1()4(21

~11

1~

11

b

Tb

z

cjcrcih

RCX

Unknown in numerator will be obtained by regression

Determining the Time Constants (1)

Canceling RCX yields the regression equation

)4(21

)4(21

)4(21

)4(21

)4(21

)4(21

~1

~1

~1

~1

~1

~1

b

b

b

bbb

z

zxxrf

z

zzconj

hyyrf

with variables

xxrfcjcrci

cjcrciyyrfTT

)1()1(

1

The zero intercept allows for the computation of RCX

Determining the Time Constants (2)

can be computed by deembedding raw data with the known RCX. The coefficients with the

time constants are obtained by regression from

)3(21

~eh

)1(2

)1(021

)3(21

)1()3()3(21

~1

~1

1~1

~11

Tee

TTe

cjcrci

hh

cjcrcih

)1(TQuadratic for and then regression povides 0

cjcrci

gives correct transit time in full bias range

)3(21

~eh

Example: main regression

0 1 2 3 4 5 6 7

x 1011

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

-10

yyrf

[s]

xxrf [s]

f1dd06 meas.: tau1+tci & tau1*tci extraction: Vce=7.001V

Vbe= 0.750VVbe= 0.755VVbe= 0.760VVbe= 0.765VVbe= 0.770VVbe= 0.775VVbe= 0.780VVbe= 0.785VVbe= 0.790VVbe= 0.795VVbe= 0.800V

The high linearity is confirming the concept

Example: Averaging RCX

0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.820

100

200

300

400

500

600

Vbe [V]

RC

X [o

hms*

um]

f1ddo8 meas. RCX

RCX= 78ohms*um

Vce= 7.00VVce= 10.00V

0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.820

100

200

300

400

500

600

Vbe [V]R

CX

[ohm

s*um

]

f1dd24 meas. RCX

RCX= 496ohms*um

Vce= 7.00VVce= 10.00V

RCX of a short (Le=0.8um) and a long (Le=24um) device

Example: RCX from parasitic PNP

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.310

-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

VBC [V]

ISU

B [A

/um

]

Regressed ISUB : n221_0.8

ISP= 1.401e-17 NFP= 1.0000 IKP= 1.026e-05 RBX= 102.6 RCX= 60.4

IS_FGPIS_RG

A perfect fit to measurements

Example: RF and DC Comparision

0 5 10 15 20 2550

100

150

200

250

300

350

400

450

500

Le [um]

RC

X_R

F, R

CX

_DC

[ohm

s*um

]

RCX extracted by RF and DC, on double collector, single base transistors

RCX_RFRBX_DC

Only a part of RCX is in the Isub current path

The difference may be particularly critical for HICUM!

Example: Time constants (1)

0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.820.8

1

1.2

1.4

1.6

1.8

2

2.2x 10

-11

tau1

+tci

[s]

Vbe [V]

f1dd06 meas. tau1+tci

Vce= 7.00VVce= 10.00V

Transit time of unilateralized Block#3

Example: Time constants (2)

0.75 0.755 0.76 0.765 0.77 0.775 0.784

6

8

10

12

14

16

18

(1

) , rci

*cjc

[ps]

Vbe [V]

f1ddu6 meas. transit time components (Vce= 7.00V)

(1)

rci*cjc

Intrinsic and collector time constants from quadratic

Example: Extraction of 0

0 500 1000 15000

5

10

15

20

25

Vt/Ic [ohms*um]

1/

(1) , 1

/(4

) [ps]

f1ddu6 meas. low current transit times (Vce= 7.00V)

0(1)= 0.79ps

0(4)= 7.29ps

1/(1)

1/(4)

Raw and intrinsic low current transit times

Lowlights

• The method mines data from the full depth of the model: high quality low noise RF data is reqired

• The quadratic may provide complex roots at higher biases: not critical since a few points are enough for 0 regression

Highlights

• The method is unprecedented as to jointly extract RBX with the intrinsic low-bias time constant

• No former model parameters are needed

• Self-consistency is insured by using one single data

• HICUM preference is met by extracting critical parameters from RF measurements

• The firm theoretical basis may provide confidence in customers and modeling engineers

Correct transit times in full bias range from one single raw s-parameter set!

Suggestion to the Model Developers

• Revive the discussion of the low-bias collector time constant in the model documentation

• Advise a proper way how to merge the collector time-constant in the present model structure

Acknowledgement

The author is grateful to

for the careful measurement of the samples and designing the setup & codes for a noiseless substrate

current acquisition.

Dr. Bishwanat Senapati